Search results

This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loe`ve spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra. ; The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program "Return of German scientists from abroad". The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241.

We propose a new detector of primary users in cognitive radio networks. The main novelty of the proposed detector in comparison to most known detectors is that it is based on sound statistical principles for detecting cyclostationary signals. In particular, the proposed detector is (asymptotically) the locally most powerful invariant test, i.e. the best invariant detector for low signal-to-noise ratios. The derivation is based on two main ideas: the relationship between a scalar-valued cyclostationary signal and a vector-valued wide-sense stationary signal, and Wijsman's theorem. Moreover, using the spectral representation for the cyclostationary time series, the detector has an insightful interpretation, and implementation, as the broadband coherence between frequencies that are separated by multiples of the cycle frequency. Finally, simulations confirm that the proposed detector performs better than previous approaches. ; The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program "Return of German scientists from abroad". The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241.

We derive the generalized likelihood ratio test (GLRT) for detecting cyclostationarity in scalar- valued time series. The main idea behind our approach is Gladyshev's relationship, which states that when the scalar-valued cyclostationary signal is blocked at the known cycle period it produces a vectorvalued wide-sense stationary (WSS) process. This result amounts to saying that the covariance matrix of the vector obtained by stacking all observations of the time series is block-Toeplitz if the signal is cyclostationary, and Toeplitz if the signal is wide-sense stationary. The derivation of the GLRT requires the maximum likelihood estimates of Toeplitz and block-Toeplitz matrices. This can be managed asymptotically (for large number of samples) exploiting Szegö's theorem and its generalization for vector-valued processes. Simulation results show the good performance of the proposed GLRT. ; The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project COSIMA (TEC2010-19545-C04-03) and project COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 Program). The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program "Return of German scientists from abroad.

We derive an estimator of the cycle period of a univariate cyclostationary process based on an information-theoretic criterion. Transforming the univariate cyclostationary process into a vector-valued wide-sense stationary process allows us to obtain the structure of the covariance matrix, which is block-Toeplitz, and its block size depends on the unknown cycle period. Therefore, we sweep the block size and obtain the ML estimate of the covariance matrix, required for the information-theoretic criterion. Since there are no closed-form ML estimates of block-Toeplitz matrices, we asymptotically approximate them as block-circulant. Finally, some numerical examples show the good performance of the proposed estimator. ; The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program "Return of German scientists from abroad". The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241.

Much of the recent work on multiantenna spectrum sensing in cognitive radio (CR) networks has been based on generalized likelihood ratio test (GLRT) detectors, which lack the ability to learn from past decisions and to adapt to the continuously changing environment. To overcome this limitation, in this paper we propose a Bayesian detector capable of learning in an efficient way the posterior distributions under both hypotheses. These posteriors summarize, in a compact way, all information seen so far by the cognitive secondary user. Our Bayesian model places priors directly on the spatial covariance matrices under both hypothesis, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypothesis, respectively; and a binomial distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior for the channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which forms the basis of the proposed Bayesian learning procedure. We also include a forgetting mechanism that allows to operate satisfactorily on time-varying scenarios. The performance of the Bayesian detector is evaluated by simulations and also by means of CR testbed composed of universal radio peripheral (USRP) nodes. Both the simulations and our experimental measurements show that the Bayesian detector outperforms the GLRT in a variety of scenarios. ; The research leading to these results has received funding from the Spanish Government (MIC INN) under Projects TEC2010-19545-C04-03 (COSIMA) and CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS). It also has been supported by FPI Grant BES-2011-047647.

In this paper we employ a 2×2 Multiple-Input Multiple-Output (MIMO) hardware platform to evaluate, in realistic indoor scenarios, the performance of different space-time block coded (STBC) transmissions at 2.4GHz. In particular, we focus on the Alamouti orthogonal scheme considering two types of channel state information (CSI) estimation: a conventional pilot-aided supervised technique and a recently proposed blind method based on second-order statistics (SOS). For comparison purposes, we also evaluate the performance of a Differential (non-coherent) space-time block coding (DSTBC). DSTBC schemes have the advantage of not requiring CSI estimation but they incur in a 3dB loss in performance. The hardware MIMO platform is based on high-performance signal acquisition and generation boards, each one equipped with a 1GB memory module that allows the transmission of extremely large data frames. Upconversion to RF is performed by two RF vector signal generators whereas downconversion is carried out with two custom circuits designed from commercial components. All the baseband signal processing is implemented off-line in MATLAB®, making the MIMO testbed very flexible and easily reconfigurable. Using this platform we compare the performance of the described methods in line-of-sight (LOS) and non-line-of-sight (NLOS) indoor scenarios. ; This work has been supported by Ministerio de Educación y Ciencia of Spain, Xunta de Galicia and FEDER funds of the European Union under grant numbers TEC2004-06451-C05-02, TEC2004-06451-C05-01, PGIDT05PXIC10502PN, and FPU grants AP2004-5127 and AP2006-2965.